PSAT Math Multiple-Choice Question 692: Answer and Explanation

Question: 692

Andrew rides his bike 20 miles directly north and then 15 miles directly to the east. How many miles would he travel if he could fly directly from his starting point to his ending point?

• A. 25
• B. 31
• C. 35
• D. 625

Correct Answer: A

Explanation:

(A) The length Andrew would fly would simply be the hypotenuse of a right triangle with side lengths of 20 miles and 15 miles. So we can use the Pythagorean theorem, which states that a² + b² = c², where a and b represent the sides and c represents the hypotenuse:

(20)² + (15)² = c²

400 + 225 = c²

Choice (A) is correct.

Alternatively, you could have saved a bit of time by noticing that this is just a variation of a 3-4-5 triangle:

15 = 3(5) and 20 = 4(5)

Thus, the hypotenuse will be 5(5) or 25.